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3 years ago

Two lines and a point Are guaranteed to be coplanar if

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

7 0

If they are parallel and intersecting

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Emily makes 75 pins to sell at the school craft fair. She has two designs: a star and

irakobra [83]

Answer:

45 bumblebee, 30 star.

Step-by-step explanation:

2:3 = 5

75/5 = 15

15 X 2= 30

15 X 3= 45

3 0

3 years ago

What is the inverse of the functionf(x)=2x+1

mr Goodwill [35]

x = 2x + 1

x - 2x = 1

-x = 1

x = -1

3 0

4 years ago

Read 2 more answers

If cos() = − 2 3 and is in Quadrant III, find tan() cot() + csc(). Incorrect: Your answer is incorrect.

nydimaria [60]

Answer:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

Step-by-step explanation:

Given

$\cos(\theta) = -\frac{2}{3}$

$\theta \to$ Quadrant III

Required

Determine $\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

We have:

$\cos(\theta) = -\frac{2}{3}$

We know that:

$\sin^2(\theta) + \cos^2(\theta) = 1$

This gives:

$\sin^2(\theta) + (-\frac{2}{3})^2 = 1$

$\sin^2(\theta) + (\frac{4}{9}) = 1$

Collect like terms

$\sin^2(\theta) = 1 - \frac{4}{9}$

Take LCM and solve

$\sin^2(\theta) = \frac{9 -4}{9}$

$\sin^2(\theta) = \frac{5}{9}$

Take the square roots of both sides

$\sin(\theta) = \±\frac{\sqrt 5}{3}$

Sin is negative in quadrant III. So:

$\sin(\theta) = -\frac{\sqrt 5}{3}$

Calculate $\csc(\theta)$

$\csc(\theta) = \frac{1}{\sin(\theta)}$

We have: $\sin(\theta) = -\frac{\sqrt 5}{3}$

So:

$\csc(\theta) = \frac{1}{-\frac{\sqrt 5}{3}}$

$\csc(\theta) = \frac{-3}{\sqrt 5}$

Rationalize

$\csc(\theta) = \frac{-3}{\sqrt 5}*\frac{\sqrt 5}{\sqrt 5}$

$\csc(\theta) = \frac{-3\sqrt 5}{5}$

So, we have:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \tan(\theta) \cdot \frac{1}{\tan(\theta)} + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 + \csc(\theta)$

Substitute: $\csc(\theta) = \frac{-3\sqrt 5}{5}$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 -\frac{3\sqrt 5}{5}$

Take LCM

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

6 0

3 years ago

Find the total surface area of this cone.

julsineya [31]

Answer:

A = πr² = B

A = π(8)² = B

A = (3.14)(64) = B

A = 200.96 m = B

A = πrl + B

A = π(8)(25) + 201

A = 628 + 201

A = 829 m

7 0

3 years ago

A cube-shaped hole is cut in a rectangular prism as shown below.

IgorC [24]

Surface area of the prism is 2xy+2xz+2yz
I think, we can cut hole on the face of the prisma 40x30, and size of the whole will be 5X5X5
hole increases surface area. If side of the cube is "a", then a^2 is the area of the one face of the cube.
when we are doing the hole, we remove 2 faces and add 4 more faces, so
2xy+2xz+2yz-2a^2+4a^2= 2xy+2xz+2yz+2a^2
So, 2*5*40+2*5*30+2*40*30+2*5^2=3150 cm^2
i hope it helps, it is what i can come up with now

6 0

4 years ago

Read 2 more answers